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Square Root of 107

The square root of 107 is expressed as √107 in the radical form and as (107)^½ or (107)^0.5 in the exponent form. The square root of 107 rounded up to 6 decimal places is 10.344080. It is the positive solution of the equation x² = 107.

Square Root of 107: 10.344080432788601
Square Root of 107 in exponential form: (107)^½ or (107)^0.5
Square Root of 107 in radical form: √107

Square Root of 107

1.	What is the Square Root of 107?
2.	How to find the Square Root of 107?
3.	Is the Square Root of 107 Irrational?
4.	FAQs

What is the Square Root of 107?

The square root of 107, (or root 107), is the number which when multiplied by itself gives the product as 107. Therefore, the square root of 107 = √107 = 10.344080432788601.

☛ Check: Square Root Calculator

How to Find Square Root of 107?

Square Root of 107 by Long Division Method

Value of √107 by Long Division Method

Explanation:

Forming pairs: 01 and 07
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 07, to the right of the remainder 0. The new dividend is now 7.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 0) such that 2Z × Z <= 7. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 7.
Divide 7 by 20 with the quotient as 0, giving the remainder = 7 - 20 × 0 = 7 - 0 = 7.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 7. The new dividend is now 700.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 3) such that 20Z × Z <= 700. Together they form a new divisor (203) for the new dividend (700).
Divide 700 by 203 with the quotient as 3, giving the remainder = 700 - 203 × 3 = 700 - 609 = 91.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 107.

Therefore, the square root of 107 by long division method is 10.3 approximately.

Is Square Root of 107 Irrational?

The actual value of √107 is undetermined. The value of √107 up to 25 decimal places is 10.34408043278860046973860. Hence, the square root of 107 is an irrational number.

☛ Also Check:

Square Root of 625 - √625 = 25
Square Root of 841 - √841 = 29
Square Root of 1681 - √1681 = 41
Square Root of 42 - √42 = 6.48074
Square Root of 140 - √140 = 11.83216
Square Root of 1024 - √1024 = 32
Square Root of 41 - √41 = 6.40312

Square Root of 107 Solved Examples

Example 1: Solve the equation x² − 107 = 0

Solution:

x² - 107 = 0 i.e. x² = 107
x = ±√107
Since the value of the square root of 107 is 10.344,
⇒ x = +√107 or -√107 = 10.344 or -10.344.
Example 2: If the surface area of a cube is 642 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 642 in²
⇒ a = ±√107 in
Since length can't be negative,
⇒ a = √107
We know that the square root of 107 is 10.344.
⇒ a = 10.344 in
Example 3: If the area of a circle is 107π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 107π in²
⇒ r = ±√107 in
Since radius can't be negative,
⇒ r = √107
The square root of 107 is 10.344.
⇒ r = 10.344 in

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FAQs on the Square Root of 107

What is the Value of the Square Root of 107?

The square root of 107 is 10.34408.

Why is the Square Root of 107 an Irrational Number?

The number 107 is prime. This implies that the number 107 is pairless and is not in the power of 2. Therefore, the square root of 107 is irrational.

What is the Value of 18 square root 107?

The square root of 107 is 10.344. Therefore, 18 √107 = 18 × 10.344 = 186.193.

Evaluate 19 plus 13 square root 107

The given expression is 19 + 13 √107. We know that the square root of 107 is 10.344. Therefore, 19 + 13 √107 = 19 + 13 × 10.344 = 19 + 134.473 = 153.473

What is the Square Root of -107?

The square root of -107 is an imaginary number. It can be written as √-107 = √-1 × √107 = i √107 = 10.344i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 107?

The square of the square root of 107 is the number 107 itself i.e. (√107)² = (107)^2/2 = 107.

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